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Dynamics of pearling instability in polymersomes: the role of shear membraneviscosity and spontaneous curvature

The stability of copolymer tethers is investigated theoretically. Self-assembly of diblockor triblock copolymers can lead to tubular polymersomes which are known experimentallyto undergo shape instability under thermal, chemical and tension stresses. It leads to aperiodic modulation of the radius which evolves to assembly-line pearls connected by tinytethers. We study the contributions of shear surface viscosity and spontaneous curvatureand their interplay to understand the pearling instability. The performed linear analysisof stability of this cylinder-to-pearls transition shows that such systems are unstable if themembrane tension is larger than a finite critical value contrary to the Rayleigh-Plateau in-stability, an already known or if the spontaneous curvature is in a specific range whichdepends on membrane tension. For the case of spontaneous curvature-induced shape insta-bility, two dynamical modes are identified. The first one is analog to the tension-inducedinstability with a marginal mode. Its wavenumber associated to the most unstable modedecreases continuously to zero as membrane viscosity increases. The unexpected secondone has a finite range of unstable wavenumbers. The wavenumber of the most unstablemode tends to a constant as membrane viscosity increases. In this mode, its growth ratebecomes independent of the bulk viscosity in the limit of high membrane viscosity andbehaves as a pure viscous surface.